Swimming mediated by ciliary beating: comparison with a squirmer model

Abstract

The squirmer model of Lighthill and Blake has been widely used to analyse swimming ciliates. However, real ciliates are covered by hair-like organelles, called cilia; the differences between the squirmer model and real ciliates remain unclear. Here, we developed a ciliate model incorporating the distinct ciliary apparatus, and analysed motion using a boundary element–slender-body coupling method. This methodology allows us to accurately calculate hydrodynamic interactions between cilia and the cell body under free-swimming conditions. Results showed that an antiplectic metachronal wave was optimal in the swimming speed with various cell-body aspect ratios, which is consistent with former theoretical studies. Exploiting oblique wave propagation, we reproduced a helical trajectory, like Paramecium, although the cell body was spherical. We confirmed that the swimming velocity of model ciliates was well represented by the squirmer model. However, squirmer modelling outside the envelope failed to estimate the energy costs of swimming; over 90 % of energy was dissipated inside the ciliary envelope. The optimal swimming efficiency was given by the antiplectic wave; the value was 6.7 times larger than in-phase beating. Our findings provide a fundamental basis for modelling swimming micro-organisms.

Swimming with swirl in a viscoelastic fluid

“…We further remark that comparisons of power and efficiency for swimmers having different gaits (i.e. different values of and ) should be undertaken with caution given recent results suggesting that the squirmer model underestimates the true power expenditure of swimming microorganisms (Ito, Omori & Ishikawa 2019).

Figure 12.Normalized hydrodynamic power and efficiency as a function of Wi and degree of swirl, , for a neutral squirmer ().

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Squirmers with swirl at low Weissenberg number

“…In summary, we utilize the spherical squirmer model for viscoelastic ambient fluids, namely (2.1)–(2.3) with . We also mention here that the suitability of the steady-state squirmer model for the study of real micro-swimmers in biological Newtonian systems has been investigated by Ito, Omori & Takuji (2019). These authors concluded that the steady squirmer model can predict very well the swimming speed of the body but drastically underestimates the power consumption, i.e.…”

Optimal slip velocities of micro-swimmers with arbitrary axisymmetric shapes

“…Vilfan (2012) optimized the steady slip velocity and the shape at the same time, with constraints on its volume and maximum curvature. The work considered power loss not only outside but also inside the squirmer surface, which could be an order of magnitude higher than the outside power loss alone (Keller & Wu 1977;Ito et al 2019). However, it assumed that the tangential force on the squirmer surface is linear to its local slip velocity, which is not always the case for microswimmers.…”